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In this paper, we present a study of thermal, average power scaling, change in index of refraction and stress in photonic crystal fiber lasers with different pump schemes: forward pump scheme, backward pump scheme, forward pump scheme with reflection of 98%, backward pump scheme with reflection of 98% and bi-directional pump scheme. We show that management of thermal effects in fiber lasers will determine the efficiency and success of scaling-up efforts. In addition, we show that the most suitable scheme is the bi-directional.

The superiorities of the conventional solid-state and gas lasers make Yb^{3+} doped fibers lasers reported [^{3+} surrounded by a lower index cladding, which is, surrounded by an air-clad region, in turn, surrounded by a second lower index cladding index.

By analytical and numerical calculation and using the finite-difference method (FDM), we have determined the expressions of temperature distribution in different regions of the photonic crystal fiber laser (PCF) along the axial and radial directions from the integration of the steady-state heat equation for an isotropic medium. Then we used the expressions previously derived for the temperatures in Regions I, II, III, and IV [

The resulting gradients are still small as the corresponding stress values. As a consequence, we expect that changes in the index of refraction due to the stress-optic effect will be negligible in different pump schemes, and thermally induced birefringence will be absent in fiber lasers (in all cases of pumping), the stress component ^{−6} kg/m^{2} and −3.4 ´ 10^{−6} kg/m^{2} in the four primer cases. Moreover, in the case bi-directional pump scheme, its value is between −0.8 ´ 10^{−6} kg/m^{2} and −1.8 ´ 10^{−6} kg/m^{2}. And the values of the change in index of refraction increases in the cases of forward pump schemes and decreases in the cases of the backward pump schemes, along the fiber laser. For the bi-directional, its value is even smaller.

As shown in ^{3+}-doped double-clad PCF laser consists of an Yb^{3+}-doped dou- ble PCF with reflectors on both of the ends.

The temperature distribution in a fiber reported in [

We calculate the average temperature

where

where the temperature expressions

And

The length of the optical fibers is much greater than a typical fiber outside radius (b), we can invoke the plane- strain approximation [

in the case where the fiber end faces are free of traction

where

where.

It can be shown that (13)-(24) satisfy the boundary conditions

will be used in Section IV under to calculate the radially varying index of refraction in different pump schemes, due to the stress-optic effect. Note that the equations as derived above for the fiber stresses could also have been obtained by use of the deviation of the temperature distribution from the average and the Airy stress potential [

Using the expressions for the radial temperature distributions, reported [

where

As before, the roman numerals refer to Regions I, II, III and IV. Here, we will calculate

For Regions I, II, III and IV, becomes

And

And

And

The calculation of the stress-induced index changes

Using

where

We can also define the brief ringence

Which may be calculated by using, yielding

Equations (56)-(59) show that the fiber birefringence depends only on the thermally induced stresses. Finally, by using (43)-(50) and substituting (13)-(20) for the radial, tangential, and

Where

For simplicity, we concentrated in this work on Yb^{3+}. The core region is surrounded by a circle inner cladding region with dimensions of radius 125 µm, the width of air-clad is 5 µm and which is in turn surrounded by a polymeric outer cladding region with outside diameter of about 300 µm.

In Figures 3(a)-(e), we plotted the stress components radial, tangential and longitudinal as a function of the radial coordinate r in different pump schemes for a Yb^{3+} fiber with a pump of 200 W, b = 300 µm is the outer radius, convective coefficient h = 40.9 W/cm×K. The quantities

For more clarification, we plotted the stress components as a function of the radius in different pump schemes. In Figures 4(a)-(e), we observe that there is a rapid increase in air-clad region of the components radial

Using (47)-(54), we plotted the tangential and the radial indices of refraction as a function of the radial coordinate r in different pump schemes, Figures 5(a)-(e), the pump power used is 200 W, the fiber outside radius is b = 300 µm, and the convection coefficient is h = 40.9 W/m×K, and

and

crease along the fiber lasers in ^{−3} to 0.1 × 10^{−3}. In ^{−3} to 1.2 × 10^{−3}. Nevertheless, in ^{−3} to 7 × 10^{−3}. As result, we notice in side of

pumping there is a small difference of the change in index of refraction between the fiber core r = 0 and in the outer clad r = b, the four Figures 5(a)-(d). However, in

In this paper, we have investigated a comparison of stress and thermo-optic of photonic crystal fiber (PCFs) in different pump schemes. Using in these calculations a simple model of (PCFs) and finite differential method (FDM), we have revealed the temperature in the core of the fiber and by laws of heat transfer, we determined its value at the surface of the fiber and the stress value in the different regions of the fiber.

In summary, regarding stress, thermo-optic and the change in index of refraction, their value does not have a great effect on the quality of the laser beam in different pump schemes, especially in the case of the bi-direc- tional pumping. Hence, after this investigation, we proved the architecture of laser cavity that was the most convenient in specific condition. The bi-directional pump scheme is the most suitable because it has less thermal effects than the other cases. However, the backward pump with reflection of 98% and the forward pump with reflection of 98% save more energy than the backward pump with reflection of 0%, the forward pump with ref- lection of 0% and bi-directional pump scheme.